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Dan Vilenchik

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I received the Ph.D. degree in computer science from Tel-Aviv University, Israel, in 2009. I am currently a lecturer at Ben-Gurion University in Israel at the department of communication systems engineering. My research interests include machine learning, optimization, and computational statistics.

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Olivia Akposibruke

Cecilia Mascolo

University of Cambridge

Ben Gurion University of the Negev

David Nettleton

Pompeu Fabra University

Akwesi Assensoh-Kodua

Durban University of Technology

Germà Coenders

University of Girona

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Papers by Dan Vilenchik

The Million Tweets Fallacy: Activity and Feedback Are Uncorrelated

Proceedings of the International AAAI Conference on Web and Social Media

In this paper we point to a surprising phenomenon in Online Social Networks (OSNs), which we call... more In this paper we point to a surprising phenomenon in Online Social Networks (OSNs), which we call "The Million Tweets Fallacy". Our hypothesis is that the measurements of activity of a user in an OSN are not correlated with the measurements of feedback that the user receives on that activity. For example, the number of tweets is uncorrelated with the number of retweets or likes. In other words, a voluminously tweeting user is not necessarily fuelled by the attention he gets from his followers. An innovative aspect of this work is that we treat "activity" and "feedback" as multidimensional axes, and do not reduce the problem to a one-dimensional pairwise correlation problem. We apply our methodology to six OSNs. For Twitter, Instagram, LinkedIn and Steam we gathered the data ourselves, collecting features that cover both users' activity and feedback in the OSN. For YouTube and Flickr we used existing data from the literature. In all OSNs, with the on...

Opinion Spam Detection: A New Approach Using Machine Learning and Network-Based Algorithms

Proceedings of the International AAAI Conference on Web and Social Media

E-commerce is the fastest-growing segment of the economy. Online reviews play a crucial role in h... more E-commerce is the fastest-growing segment of the economy. Online reviews play a crucial role in helping consumers evaluate and compare products and services. As a result, fake reviews (opinion spam) are becoming more prevalent and negatively impacting customers and service providers. There are many reasons why it is hard to identify opinion spammers automatically, including the absence of reliable labeled data. This limitation precludes an off-the-shelf application of a machine learning pipeline. We propose a new method for classifying reviewers as spammers or benign, combining machine learning with a message-passing algorithm that capitalizes on the users' graph structure to compensate for the possible scarcity of labeled data. We devise a new way of sampling the labels for the training step (active learning), replacing the typical uniform sampling. Experiments on three large real-world datasets from Yelp.com show that our method outperforms state-of-the-art active learning app...

Routledge eBooks, Nov 7, 2022

The Mind of a Killer

Routledge eBooks, Nov 7, 2022

The Compositionality of Facial Expressions

Perception, 2022

The principle of compositionality, an important postulation in language and cognition research, p... more The principle of compositionality, an important postulation in language and cognition research, posits that the meaning of a complex expression is determined by the meaning of its constituting parts and the operation performed on those parts. Here, we provide strong evidence that this principle plays a significant role also in interpreting facial expressions. In three studies in which perceivers interpreted sequences of two emotional facial expression images, we show that the composite meaning of facial expressions results from the meaning of its constituting expressions and an algebraic operation performed on those expressions. Our study offers a systematic account as to how the meaning of facial expressions (single and sequences) are being formed and perceived. In a broader context, our results raise the possibility that the principle of compositionality may apply to human communication modalities beyond spoken language, whereby a minimal number of components are expanded to a muc...

Welfare vs. Representation in Participatory Budgeting

Participatory budgeting (PB) is a democratic process for allocating funds to projects based on th... more Participatory budgeting (PB) is a democratic process for allocating funds to projects based on the votes of members of the community. Different rules have been used to aggregate participants' votes. Past research has studied the trade-off between notions of social welfare and fairness in the multi-winner setting (a special case of participatory budgeting with identical project costs) by Lackner and Skowron (2020). But there is little understanding of this trade-off in the more general PB setting. This paper provides a theoretical and empirical study of the worst-case guarantees of several common rules to better understand the trade-off between social welfare, representation. We show that many of the guarantees from the multi-winner setting do not generalize to the PB setting, and that the introduction of costs leads to substantially worse guarantees, thereby exacerbating the welfare-representation trade-off. We extend our theoretical analysis to studying how the requirement of p...

An Oblivious Approach to Machine Translation Quality Estimation

Mathematics, 2021

Machine translation (MT) is being used by millions of people daily, and therefore evaluating the ... more Machine translation (MT) is being used by millions of people daily, and therefore evaluating the quality of such systems is an important task. While human expert evaluation of MT output remains the most accurate method, it is not scalable by any means. Automatic procedures that perform the task of Machine Translation Quality Estimation (MT-QE) are typically trained on a large corpus of source–target sentence pairs, which are labeled with human judgment scores. Furthermore, the test set is typically drawn from the same distribution as the train. However, recently, interest in low-resource and unsupervised MT-QE has gained momentum. In this paper, we define and study a further restriction of the unsupervised MT-QE setting that we call oblivious MT-QE. Besides having no access no human judgment scores, the algorithm has no access to the test text’s distribution. We propose an oblivious MT-QE system based on a new notion of sentence cohesiveness that we introduce. We tested our system o...

OUP accepted manuscript

Nucleic Acids Research, 2021

DNA–protein interactions play essential roles in all living cells. Understanding of how features ... more DNA–protein interactions play essential roles in all living cells. Understanding of how features embedded in the DNA sequence affect specific interactions with proteins is both challenging and important, since it may contribute to finding the means to regulate metabolic pathways involving DNA–protein interactions. Using a massive experimental benchmark dataset of binding scores for DNA sequences and a machine learning workflow, we describe the binding to DNA of T7 primase, as a model system for specific DNA–protein interactions. Effective binding of T7 primase to its specific DNA recognition sequences triggers the formation of RNA primers that serve as Okazaki fragment start sites during DNA replication.

The Adaptive Behavior of a Soccer Team: An Entropy-Based Analysis

Entropy, 2018

To optimize its performance, a competitive team, such as a soccer team, must maintain a delicate ... more To optimize its performance, a competitive team, such as a soccer team, must maintain a delicate balance between organization and disorganization. On the one hand, the team should maintain organized patterns of behavior to maximize the cooperation between its members. On the other hand, the team’s behavior should be disordered enough to mislead its opponent and to maintain enough degrees of freedom. In this paper, we have analyzed this dynamic in the context of soccer games and examined whether it is correlated with the team’s performance. We measured the organization associated with the behavior of a soccer team through the Tsallis entropy of ball passes between the players. Analyzing data taken from the English Premier League (2015/2016), we show that the team’s position at the end of the season is correlated with the team’s entropy as measured with a super-additive entropy index. Moreover, the entropy score of a team significantly contributes to the prediction of the team’s posit...

From physical to social interactions: The relative entropy model

Scientific Reports, 2020

Complex social systems at various scales of analysis (e.g. dyads, families, tribes, etc.) are for... more Complex social systems at various scales of analysis (e.g. dyads, families, tribes, etc.) are formed and maintained through verbal interactions. Therefore, the ability to (1) model these interactions and (2) to use models of interaction for identifying significant relations may be of interest to the social sciences. Adopting the perspective of social physics, we present a general approach for modeling interactions through relative entropy. For illustrating the benefits of the approach, we derive measures of “perspective-taking” and use them for identifying significant-romantic relations in a data set composed of the verbal interactions taken place at the famous TV series “Sex and the City”. Using these measures, we show that significant-romantic relations can be identified with success. These results provide preliminary support for the benefits of using the proposed approach.

Modeling Small Systems through the Relative Entropy Lattice

IEEE Access, 2019

There are certain contexts where we would like to analyze the behavior of small interacting syste... more There are certain contexts where we would like to analyze the behavior of small interacting systems, such as sports teams. While large interacting systems have drawn much attention in the past years, let it be physical systems of interacting particles or social networks, small systems are short of appropriate quantitative modeling and measurement tools. We propose a simple procedure for analyzing a small system through the degree in which its behavior at different granularity levels (e.g. dyads) non-linearly diverges from the simple additive behavior of its sub-units. For example, we may model the behavior of a soccer team by measuring the extent to which the behavior changes when we move from individual players to dyads, triads and so on. In this paper, we address the challenge of modeling small systems in terms of measuring divergence from additivity at different granularity levels of the system. We present and develop a measure for quantifying divergence from additivity through what we term a Relative Entropy Lattice, and illustrate its benefits in modeling the behavior of a specific small system, a soccer team, using data from the English Premier League. Our method has practical implications too, such as allowing the coach to identify "hidden" weak spots in the team's behavior.

Simple statistics are sometime too simple: A case study in social media data

IEEE Transactions on Knowledge and Data Engineering, 2019

Constructing cospectral graphs via a new form of graph product

Linear and Multilinear Algebra, 2017

Abstract We present a new method to construct a family of co-spectral graphs. Our method is based... more Abstract We present a new method to construct a family of co-spectral graphs. Our method is based on a new type of graph product that we define, the bipartite graph product, which may be of self-interest. Our method is different from existing techniques in the sense that it is not based on a sequence of local graph operations (e.g. Godsil–McKay switching). The explicit nature of our construction allows us, for example, to construct an infinite family of cospectral graphs and provide an easy proof of non-isomorphism. We are also able to characterize fully the spectrum of the cospectral graphs.

STEM: Unsupervised STructural EMbedding for Stance Detection

ArXiv, 2021

Stance detection is an important task, supporting many downstream tasks such as discourse parsing... more Stance detection is an important task, supporting many downstream tasks such as discourse parsing and modeling the propagation of fake news, rumors, and science denial. In this paper, we propose a novel framework for stance detection. Our framework is unsupervised and domain-independent. Given a claim and a multi-participant discussion – we construct the interaction network from which we derive topological embeddings for each speaker. These speaker embeddings enjoy the following property: speakers with the same stance tend to be represented by similar vectors, while antipodal vectors represent speakers with opposing stances. These embeddings are then used to divide the speakers into stance-partitions. We evaluate our method on three different datasets from different platforms. Our method outperforms or is comparable with supervised models while providing confidence levels for its output. Furthermore, we demonstrate how the structural embeddings relate to the valence expressed by the...

Getting directed Hamilton cycle twice faster

Consider the random graph process where we start with an empty graph on n vertices, and at time t... more Consider the random graph process where we start with an empty graph on n vertices, and at time t, are given an edge e_t chosen uniformly at random among the edges which have not appeared so far. A classical result in random graph theory asserts that w.h.p. the graph becomes Hamiltonian at time (1/2+o(1))n log n. On the contrary, if all the edges were directed randomly, then the graph has a directed Hamilton cycle w.h.p. only at time (1+o(1))n log n. In this paper we further study the directed case, and ask whether it is essential to have twice as many edges compared to the undirected case. More precisely, we ask if at time t, instead of a random direction one is allowed to choose the orientation of e_t, then whether it is possible or not to make the resulting directed graph Hamiltonian at time earlier than n log n. The main result of our paper answers this question in the strongest possible way, by asserting that one can orient the edges on-line so that w.h.p., the resulting graph ...

3 Zero vs. ε Error in Interference Channels

Traditional studies of multi-source, multi-terminal interference channels typically allow a vanis... more Traditional studies of multi-source, multi-terminal interference channels typically allow a vanishing probability of error in communication. Motivated by the study of network coding, this work addresses the task of quantifying the loss in rate when insisting on zero error communication in the context of interference channels.

On the Random Satisfiable Process

In this work we suggest a new model for generating random satisfiable k-CNF formulas. To generate... more In this work we suggest a new model for generating random satisfiable k-CNF formulas. To generate such formulas. randomly permute all 2k ( n) k possible clauses over the variables x1,...,xn, and starting from the empty formula, go over the clauses one by one, including each new clause as you go along if, after its addition, the formula remains satisfiable. We study the evolution of this process, namely the distribution over formulas obtained after scanning through the first m clauses (in the random permutation’s order). Random processes with conditioning on a certain property being respected are widely studied in the context of graph properties. This study was pioneered by Ruciński and Wormald in 1992 for graphs with a fixed degree sequence, and also by Erdős, Suen and Winkler in 1995 for triangle-free and bipartite graphs. Since then many other graph properties have been studied, such as planarity and H-freeness. Thus our model is a natural extension of this approach to the satisfi...

Solving random satisfiable 3CNF formulas in expected polynomial time

We present an algorithm for solving 3SAT instances. Several algorithms have been proved to work w... more We present an algorithm for solving 3SAT instances. Several algorithms have been proved to work whp (with high probability) for various SAT distributions. However, an algorithm that works whp has a drawback. Indeed for typical instances it works well, however for some rare inputs it does not provide a solution at all. Alternatively, one could require that the algorithm always produce a correct answer but perform well on average. Expected polynomial time formalizes this notion. We prove that for some natural distribution on 3CNF formulas, called planted 3SAT, our algorithm has expected polynomial (in fact, almost linear) running time. The planted 3SAT distribution is the set of satisfiable 3CNF formulas generated in the following manner. First, a truth assignment is picked uniformly at random. Then, each clause satisfied by it is included in the formula with probability p. Extending previous work for the planted 3SAT distribution, we present, for the first time for a satisfiable SAT ...

It’s All about the Support: A New Perspective on the Satisfiability Problem

We study a new approach to the satisfiability problem, which we call the Support Paradigm. Given ... more We study a new approach to the satisfiability problem, which we call the Support Paradigm. Given a CNF formula F and an assignment ψ to its variables we say that a literal x supports a clause C in F w.r.t. ψ if x is the only literal that evaluates to true in C. Our focus in this work will be on heuristics that obey the following general template: start at some assignment to the variables, then iteratively, using some predefined (greedy) rule, try to minimize the number of unsatisfied clauses (or the distance from some satisfying assignment) until a satisfying assignment is reached. We say that such a heuristic is part of the Support Paradigm if the greedy rule uses the support as its main criterion. We present a new algorithm in the Support Paradigm and rigorously prove its effectiveness for a certain distribution over satisfiable k-CNF formulas known as the planted distribution. One motivation for this work is recent experimental results showing that some simple variants of the RWa...

It’s all about the support: a new perspective for the satisfiability problem

The Million Tweets Fallacy: Activity and Feedback Are Uncorrelated

Proceedings of the International AAAI Conference on Web and Social Media

In this paper we point to a surprising phenomenon in Online Social Networks (OSNs), which we call... more In this paper we point to a surprising phenomenon in Online Social Networks (OSNs), which we call "The Million Tweets Fallacy". Our hypothesis is that the measurements of activity of a user in an OSN are not correlated with the measurements of feedback that the user receives on that activity. For example, the number of tweets is uncorrelated with the number of retweets or likes. In other words, a voluminously tweeting user is not necessarily fuelled by the attention he gets from his followers. An innovative aspect of this work is that we treat "activity" and "feedback" as multidimensional axes, and do not reduce the problem to a one-dimensional pairwise correlation problem. We apply our methodology to six OSNs. For Twitter, Instagram, LinkedIn and Steam we gathered the data ourselves, collecting features that cover both users' activity and feedback in the OSN. For YouTube and Flickr we used existing data from the literature. In all OSNs, with the on...

Opinion Spam Detection: A New Approach Using Machine Learning and Network-Based Algorithms

Proceedings of the International AAAI Conference on Web and Social Media

E-commerce is the fastest-growing segment of the economy. Online reviews play a crucial role in h... more E-commerce is the fastest-growing segment of the economy. Online reviews play a crucial role in helping consumers evaluate and compare products and services. As a result, fake reviews (opinion spam) are becoming more prevalent and negatively impacting customers and service providers. There are many reasons why it is hard to identify opinion spammers automatically, including the absence of reliable labeled data. This limitation precludes an off-the-shelf application of a machine learning pipeline. We propose a new method for classifying reviewers as spammers or benign, combining machine learning with a message-passing algorithm that capitalizes on the users' graph structure to compensate for the possible scarcity of labeled data. We devise a new way of sampling the labels for the training step (active learning), replacing the typical uniform sampling. Experiments on three large real-world datasets from Yelp.com show that our method outperforms state-of-the-art active learning app...

Routledge eBooks, Nov 7, 2022

The Mind of a Killer

Routledge eBooks, Nov 7, 2022

The Compositionality of Facial Expressions

Perception, 2022

The principle of compositionality, an important postulation in language and cognition research, p... more The principle of compositionality, an important postulation in language and cognition research, posits that the meaning of a complex expression is determined by the meaning of its constituting parts and the operation performed on those parts. Here, we provide strong evidence that this principle plays a significant role also in interpreting facial expressions. In three studies in which perceivers interpreted sequences of two emotional facial expression images, we show that the composite meaning of facial expressions results from the meaning of its constituting expressions and an algebraic operation performed on those expressions. Our study offers a systematic account as to how the meaning of facial expressions (single and sequences) are being formed and perceived. In a broader context, our results raise the possibility that the principle of compositionality may apply to human communication modalities beyond spoken language, whereby a minimal number of components are expanded to a muc...

Welfare vs. Representation in Participatory Budgeting

Participatory budgeting (PB) is a democratic process for allocating funds to projects based on th... more Participatory budgeting (PB) is a democratic process for allocating funds to projects based on the votes of members of the community. Different rules have been used to aggregate participants' votes. Past research has studied the trade-off between notions of social welfare and fairness in the multi-winner setting (a special case of participatory budgeting with identical project costs) by Lackner and Skowron (2020). But there is little understanding of this trade-off in the more general PB setting. This paper provides a theoretical and empirical study of the worst-case guarantees of several common rules to better understand the trade-off between social welfare, representation. We show that many of the guarantees from the multi-winner setting do not generalize to the PB setting, and that the introduction of costs leads to substantially worse guarantees, thereby exacerbating the welfare-representation trade-off. We extend our theoretical analysis to studying how the requirement of p...

An Oblivious Approach to Machine Translation Quality Estimation

Mathematics, 2021

Machine translation (MT) is being used by millions of people daily, and therefore evaluating the ... more Machine translation (MT) is being used by millions of people daily, and therefore evaluating the quality of such systems is an important task. While human expert evaluation of MT output remains the most accurate method, it is not scalable by any means. Automatic procedures that perform the task of Machine Translation Quality Estimation (MT-QE) are typically trained on a large corpus of source–target sentence pairs, which are labeled with human judgment scores. Furthermore, the test set is typically drawn from the same distribution as the train. However, recently, interest in low-resource and unsupervised MT-QE has gained momentum. In this paper, we define and study a further restriction of the unsupervised MT-QE setting that we call oblivious MT-QE. Besides having no access no human judgment scores, the algorithm has no access to the test text’s distribution. We propose an oblivious MT-QE system based on a new notion of sentence cohesiveness that we introduce. We tested our system o...

OUP accepted manuscript

Nucleic Acids Research, 2021

DNA–protein interactions play essential roles in all living cells. Understanding of how features ... more DNA–protein interactions play essential roles in all living cells. Understanding of how features embedded in the DNA sequence affect specific interactions with proteins is both challenging and important, since it may contribute to finding the means to regulate metabolic pathways involving DNA–protein interactions. Using a massive experimental benchmark dataset of binding scores for DNA sequences and a machine learning workflow, we describe the binding to DNA of T7 primase, as a model system for specific DNA–protein interactions. Effective binding of T7 primase to its specific DNA recognition sequences triggers the formation of RNA primers that serve as Okazaki fragment start sites during DNA replication.

The Adaptive Behavior of a Soccer Team: An Entropy-Based Analysis

Entropy, 2018

To optimize its performance, a competitive team, such as a soccer team, must maintain a delicate ... more To optimize its performance, a competitive team, such as a soccer team, must maintain a delicate balance between organization and disorganization. On the one hand, the team should maintain organized patterns of behavior to maximize the cooperation between its members. On the other hand, the team’s behavior should be disordered enough to mislead its opponent and to maintain enough degrees of freedom. In this paper, we have analyzed this dynamic in the context of soccer games and examined whether it is correlated with the team’s performance. We measured the organization associated with the behavior of a soccer team through the Tsallis entropy of ball passes between the players. Analyzing data taken from the English Premier League (2015/2016), we show that the team’s position at the end of the season is correlated with the team’s entropy as measured with a super-additive entropy index. Moreover, the entropy score of a team significantly contributes to the prediction of the team’s posit...

From physical to social interactions: The relative entropy model

Scientific Reports, 2020

Complex social systems at various scales of analysis (e.g. dyads, families, tribes, etc.) are for... more Complex social systems at various scales of analysis (e.g. dyads, families, tribes, etc.) are formed and maintained through verbal interactions. Therefore, the ability to (1) model these interactions and (2) to use models of interaction for identifying significant relations may be of interest to the social sciences. Adopting the perspective of social physics, we present a general approach for modeling interactions through relative entropy. For illustrating the benefits of the approach, we derive measures of “perspective-taking” and use them for identifying significant-romantic relations in a data set composed of the verbal interactions taken place at the famous TV series “Sex and the City”. Using these measures, we show that significant-romantic relations can be identified with success. These results provide preliminary support for the benefits of using the proposed approach.

Modeling Small Systems through the Relative Entropy Lattice

IEEE Access, 2019

There are certain contexts where we would like to analyze the behavior of small interacting syste... more There are certain contexts where we would like to analyze the behavior of small interacting systems, such as sports teams. While large interacting systems have drawn much attention in the past years, let it be physical systems of interacting particles or social networks, small systems are short of appropriate quantitative modeling and measurement tools. We propose a simple procedure for analyzing a small system through the degree in which its behavior at different granularity levels (e.g. dyads) non-linearly diverges from the simple additive behavior of its sub-units. For example, we may model the behavior of a soccer team by measuring the extent to which the behavior changes when we move from individual players to dyads, triads and so on. In this paper, we address the challenge of modeling small systems in terms of measuring divergence from additivity at different granularity levels of the system. We present and develop a measure for quantifying divergence from additivity through what we term a Relative Entropy Lattice, and illustrate its benefits in modeling the behavior of a specific small system, a soccer team, using data from the English Premier League. Our method has practical implications too, such as allowing the coach to identify "hidden" weak spots in the team's behavior.

Simple statistics are sometime too simple: A case study in social media data

IEEE Transactions on Knowledge and Data Engineering, 2019

Constructing cospectral graphs via a new form of graph product

Linear and Multilinear Algebra, 2017

Abstract We present a new method to construct a family of co-spectral graphs. Our method is based... more Abstract We present a new method to construct a family of co-spectral graphs. Our method is based on a new type of graph product that we define, the bipartite graph product, which may be of self-interest. Our method is different from existing techniques in the sense that it is not based on a sequence of local graph operations (e.g. Godsil–McKay switching). The explicit nature of our construction allows us, for example, to construct an infinite family of cospectral graphs and provide an easy proof of non-isomorphism. We are also able to characterize fully the spectrum of the cospectral graphs.

STEM: Unsupervised STructural EMbedding for Stance Detection

ArXiv, 2021

Stance detection is an important task, supporting many downstream tasks such as discourse parsing... more Stance detection is an important task, supporting many downstream tasks such as discourse parsing and modeling the propagation of fake news, rumors, and science denial. In this paper, we propose a novel framework for stance detection. Our framework is unsupervised and domain-independent. Given a claim and a multi-participant discussion – we construct the interaction network from which we derive topological embeddings for each speaker. These speaker embeddings enjoy the following property: speakers with the same stance tend to be represented by similar vectors, while antipodal vectors represent speakers with opposing stances. These embeddings are then used to divide the speakers into stance-partitions. We evaluate our method on three different datasets from different platforms. Our method outperforms or is comparable with supervised models while providing confidence levels for its output. Furthermore, we demonstrate how the structural embeddings relate to the valence expressed by the...

Getting directed Hamilton cycle twice faster

Consider the random graph process where we start with an empty graph on n vertices, and at time t... more Consider the random graph process where we start with an empty graph on n vertices, and at time t, are given an edge e_t chosen uniformly at random among the edges which have not appeared so far. A classical result in random graph theory asserts that w.h.p. the graph becomes Hamiltonian at time (1/2+o(1))n log n. On the contrary, if all the edges were directed randomly, then the graph has a directed Hamilton cycle w.h.p. only at time (1+o(1))n log n. In this paper we further study the directed case, and ask whether it is essential to have twice as many edges compared to the undirected case. More precisely, we ask if at time t, instead of a random direction one is allowed to choose the orientation of e_t, then whether it is possible or not to make the resulting directed graph Hamiltonian at time earlier than n log n. The main result of our paper answers this question in the strongest possible way, by asserting that one can orient the edges on-line so that w.h.p., the resulting graph ...

3 Zero vs. ε Error in Interference Channels

Traditional studies of multi-source, multi-terminal interference channels typically allow a vanis... more Traditional studies of multi-source, multi-terminal interference channels typically allow a vanishing probability of error in communication. Motivated by the study of network coding, this work addresses the task of quantifying the loss in rate when insisting on zero error communication in the context of interference channels.

On the Random Satisfiable Process

In this work we suggest a new model for generating random satisfiable k-CNF formulas. To generate... more In this work we suggest a new model for generating random satisfiable k-CNF formulas. To generate such formulas. randomly permute all 2k ( n) k possible clauses over the variables x1,...,xn, and starting from the empty formula, go over the clauses one by one, including each new clause as you go along if, after its addition, the formula remains satisfiable. We study the evolution of this process, namely the distribution over formulas obtained after scanning through the first m clauses (in the random permutation’s order). Random processes with conditioning on a certain property being respected are widely studied in the context of graph properties. This study was pioneered by Ruciński and Wormald in 1992 for graphs with a fixed degree sequence, and also by Erdős, Suen and Winkler in 1995 for triangle-free and bipartite graphs. Since then many other graph properties have been studied, such as planarity and H-freeness. Thus our model is a natural extension of this approach to the satisfi...

Solving random satisfiable 3CNF formulas in expected polynomial time

We present an algorithm for solving 3SAT instances. Several algorithms have been proved to work w... more We present an algorithm for solving 3SAT instances. Several algorithms have been proved to work whp (with high probability) for various SAT distributions. However, an algorithm that works whp has a drawback. Indeed for typical instances it works well, however for some rare inputs it does not provide a solution at all. Alternatively, one could require that the algorithm always produce a correct answer but perform well on average. Expected polynomial time formalizes this notion. We prove that for some natural distribution on 3CNF formulas, called planted 3SAT, our algorithm has expected polynomial (in fact, almost linear) running time. The planted 3SAT distribution is the set of satisfiable 3CNF formulas generated in the following manner. First, a truth assignment is picked uniformly at random. Then, each clause satisfied by it is included in the formula with probability p. Extending previous work for the planted 3SAT distribution, we present, for the first time for a satisfiable SAT ...

It’s All about the Support: A New Perspective on the Satisfiability Problem

We study a new approach to the satisfiability problem, which we call the Support Paradigm. Given ... more We study a new approach to the satisfiability problem, which we call the Support Paradigm. Given a CNF formula F and an assignment ψ to its variables we say that a literal x supports a clause C in F w.r.t. ψ if x is the only literal that evaluates to true in C. Our focus in this work will be on heuristics that obey the following general template: start at some assignment to the variables, then iteratively, using some predefined (greedy) rule, try to minimize the number of unsatisfied clauses (or the distance from some satisfying assignment) until a satisfying assignment is reached. We say that such a heuristic is part of the Support Paradigm if the greedy rule uses the support as its main criterion. We present a new algorithm in the Support Paradigm and rigorously prove its effectiveness for a certain distribution over satisfiable k-CNF formulas known as the planted distribution. One motivation for this work is recent experimental results showing that some simple variants of the RWa...

It’s all about the support: a new perspective for the satisfiability problem